Question

the curved surface area of a cone of slant height 50cm is 2200 cm2 . Find the volume of the cone​

Answer 1

$\bold { \red{CLARIFICATION: }}$

GIVEN :

$\mathtt{Slant \: height \: of \: the \: cone = 50 \: cm}$

$\mathtt{Curved \: surface \: area \: of \: the \: cone \: (I)=2200cm^{2}}$

TO FIND :

$\mathtt{Volume \: of \: cone = \: ?}$

SOLUTION :

Let the radius of the base of the cone be r cm

$\mathtt { \therefore \: \pi rI=2200cm ^{2}}$

$\implies \mathtt{\frac{22}{7} \times r \times 50 = 2200}$

$\implies \mathtt {\frac{2200 \times 7}{22 \times 50} = 14cm}$

We know that,

$\mathtt{Total \: Sufarce \: area \: of \: cone=πr(r+1)}$

$\implies \frac{22}{7} \times 14 \times (14 + 50)$

$\implies \frac{22}{7} \times 14 \times 64$

$\implies \mathtt {2816 \: cm^{2} }$

$\underline \mathtt {Thus \: total \: surface \: area \: of \: cone \: is \: 2816 \: cm^{2} }$

Answer 2

Given

Slant height of the cone =50cm

Curved surface area of the cone = 2200cm^2

Solution

Let the radius of the base of the cone be r cm

Therefore,

πrl =2200cm^2

22/7×r×50=2200

2200×7/22×50= 14cm

Total surface area of cone = πr(r+1)

22/7×14×(14+50)

22/7×14×64 = 2186 cm^2

Therefore Volume of cone is 2186cm^2